You Do Need power plug adapter while traveling from Falkland Islands to Western Sahara.

Here is Why You Need An Adapter

The outlet and plug type used in Western Sahara are C and E and in Falkland Islands is G. This is how they look like.

Falkland Islands

In Falkland Islands, outlets of type G are in use.

Type G

Western Sahara

In Western Sahara, outlets of type C and E are in use.

Type C

Type E